Question 19

The dimensions of a floor are $$18\times24$$. What is the smallest number of identical square tiles that pave the entire floor without the need to break any tile?

Solution

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We have dimensions : (24*18)

HCF ( 24, 18) = 6

Now Area of floor: 432

In order to minimise the number of tiles considering a tile with a dimension equivalent to the HCF,  we have the dimension of the tile to 6*6 = 36 units.

A total of $$\frac{432}{36}$$  = 12 tiles are required.

Minimum number of tiles that pave the entire floor :(LCM)^2/Area = 12

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